I haven't read the paper only looked at the first page with the two sheets, but I think the novel idea here is that it's using complementary colors.
Take a color that is maximally absorbed by the stain and thus get the most energy into it without affecting too much else.
I wonder if that would work with other colors as well.
It's an interesting idea, and how it would work with colours other than "bleached" would be the interesting part.
Presumably it wouldn't work on black without fading the garment, but given how we've seen things fade in shop windows, I wonder if there's some novel applications for removing other types of intentional "stains" like ink, or paint, and particularly if they're under/behind a surface like a clear-coat or glass or something else that prevents physical access.
I wonder if you could remove blue ink with yellow light. Specifically residue from ballpoint pens on furniture.
That would be an interesting one, I have a strangely related story that not too long ago my toddler drew _all over_ a yellow suede sofa with a blue ballpoint pen, was a nightmare to get it out without making the pristine sofa look like a drowned rat.